Mutter describes itself as a "Clutter based compositing GTK2 Window Manager" (man page). I understand that one of the goals of the Docky devs was to have Docky work with Gnome Shell, but can't remember where I read that. Anyway, it ought to run just fine under Gnome Shell.

However, Docky (which is in the Ubuntu repos) will work with almost any Desktop environment, including GNOME Shell. It also works without compositing (technically), but will just have problems drawing itself.